"The airline is the first Indian LCC to connect Mumbai with Riyadh and Dhaka and Delhi with Dhaka and Jeddah," the low-cost carrier said.
"Riyadh, the capital city of Saudi Arabia, earmarks SpiceJet's 10th international destination and the fourth station in the Middle Eastern market," it added.
Riyadh, the capital and largest city of Saudi Arabia, is also the country's key business centre and financial hub.
The flights on Mumbai-Dhaka-Mumbai route and Mumbai-Riyadh-Mumbai route will start from July 25 and August 15, respectively.
On Delhi-Dhaka-Delhi route and Delhi-Jeddah-Delhi route, the daily flights will begin from July 31, said the airline.
Ajay Singh, the chairman and managing director of SpiceJet, said, "SpiceJet is the only Indian budget airline to operate to Saudi Arabia and our new flights to Riyadh and Jeddah should greatly benefit the thousands of pilgrims travelling from India.